Warm-Up
1

What does the motion of gas
molecules look like?

Why does a balloon inflate when you
blow it up? Why will soda explode
from a bottle if opened after shaking
it?
Chapter 5
The Gas
Laws
2
Section 5.1- Pressure
Force per unit area (P = force/area).
 Gas molecules fill container.
 Molecules move around and hit
sides.
 Collisions are the force.
 Container is the area.
 Measured with a barometer.

3
How Does A Barometer Work?
Vacuum
Pressure of
atmosphere
pushes on
Hg
4
760 mm
Hg
The pressure of the
atmosphere at sea
level will cause the
column of mercury to
As a result, rise to 760 mm Hg.
Hg rises up
 1 atm = 760 mm Hg
into the glass
tube

*Hg stops rising
when it’s equal
to atmospheric
pressure
Units of pressure
1 atmosphere = 760 mm Hg
 1 mm Hg = 1 torr
 1 atm = 101,325 Pascals = 101.325 kPa

*The first two are provided on the AP
equation sheet. No need to memorize
the third- I assume you’ll be given that
if you need to use it.
5
Section 5.2
THE GAS LAWS OF BOYLE,
CHARLES, AND AVOGADRO
6
About the Laws…
You should be aware of the following
laws, however we will not focus
heavily on them as they can be
derived from the ideal gas law.
 After briefly going through each of
the following laws, we will see how to
derive each from the ideal gas law.

7
Boyle’s Law


Pressure and volume are inversely
related at constant temperature.
P1V1 = P2V2
• As one goes up, the other goes down.


Ex: if P increases (at constant T), V
must go down
Further studies show that Boyle’s Law
is only true at very low P
•

8
This will be discussed more in 5.8
Gases that obey these laws are called
ideal gases.
Charles’s Law

Volume of a gas varies directly with
the temperature at constant
pressure.

V1
V2
=
T1
T2
 As one goes up/down, so does the
other.
9
Avogadro's Law

At constant temperature and
pressure, the volume of gas is
directly related to the number of
moles.

V1
n1

10
=
V2
n2
As one goes up/down, so does the
other.
Gay- Lussac Law

At constant volume, pressure and
temperature are directly related.

P1
T1

=
T2
As one goes up/down, so does the
other.
11
P2
Combined Gas Law
Combination of Boyle’s Law, Charles’
Law, and Gay-Lussac Law.
 Moles of gas remain constant.


P1V1
T1
12
=
P2V2
T2
Summary
Boyle’s: P1V1 = P2V2
 Charles’: V1/T1 = V2/T2
 Avogadro’s: V1/n1 = V2/n2
 Gay-Lussac: P1/T1 = P2/T2
 Combined: P1V1/T1 = P2V2/T2


13
That’s a lot of laws! Or we can just
use the Ideal Gas Law!
Combined Gas Law Cont.



14
Ex: A 2.3L sample of gas has a pressure of
1.2atm at 200.K. If the pressure is raised to
1.4atm and the temperature is increased to
300.K, what is the volume of the gas?
V2 = P1V1T2
T1P2
V2 = 3.0 L
Practice

15
Ex: A 12.2L sample of gas has 0.50mol of O2 at
1atm and 25°C. How many moles of O2 would
occupy 19.4L at the same temperature and
pressure?
Solution: V1/n1 = V2/n2
(12.2L)/(0.50mol) = (19.4L)/(n2)
n2 =0.80mol
*In other words, 0.80mol of O2 would be required
to fill 19.4L in order to keep the same pressure
as 0.50mol of O2 in 12.2L.
AP Practice Question
A sample of argon gas is sealed in a
container. The volume of the
container is doubled. If the pressure
remains constant, what must happen
to the temperature?
a) It doesn’t change.
b) It is halved.
c) It is doubled.
d) It is squared.

16
Demonstration Warm-Up!
Observe the demonstration.
 Keep in mind the properties of gases
we have discussed so far: P, V, T,
and n.
 Think about these properties before
and after imploding the can. Why do
you think the can was crushed?
 As temperature decreases, so does
the pressure and volume.
 Remind you of a law we looked at?

17
Sections 1&2 Homework

18
Pgs. 217-218 #: 2, 6, 34, 35
Section 5.3
THE IDEAL GAS LAW
19
Ideal Gas Law
KNOW THIS!
PV = nRT
 At standard temperature and pressure
(STP): V = 22.4L at 1atm, 0ºC, and n =
1mol. These conditions were used to
determine R (ideal gas constant):
Choose R
»R = 0.08206 L atm/mol K
value
»= 8.314 J/mol K
according to
units of P
»= 62.36 L torr/mol K
 Tells you about a gas NOW.
 The other laws tell you about a gas when
20
it changes.

Ideal Gas Law Cont.

21
Looking back at the possible values
for R, you will notice that all units for
temperature are in K.
– When using the ideal gas law for
calculations, convert all
temperatures to K!
– Recall conversion: K = °C + 273
(provided on AP equation sheet)
Ideal Gas Law Derivation Practice
May be asked to prove one of the
laws discussed before!
 Strategy: get all constants in the
ideal gas law on one side and
changing variables on the other.
 We will go several of these in class.

22
AP Practice Question
A 1.15mol sample of carbon monoxide
gas has a temperature of 27°C and a
pressure of 0.300atm. If the
temperature is lowered to 17°C at
constant volume, what is the new
pressure?
a) 0.290atm
b) 0.519atm
23
c) 0.206atm
d) 0.338atm
Ideal Gas Law- Why ‘Ideal’?
Ideal gases are hypothetical
substances.
– Gases only approach ideal behavior
at low pressure (< 1 atm) and high
temperature.
– They do not behave exactly according
to this law, but they behave closely
enough.
– Law provides good estimates of gas
behavior under these conditions.
 Unless told otherwise, assume ideal gas
24 behavior and use the ideal gas law.

AP Practice Question

A sample of aluminum metal is
added to HCl. How many grams of
aluminum metal must be added to an
excess of HCl to produce 33.6L of
hydrogen gas at STP?
a) 18.0g
b) 35.0g
c) 27.0g
25 d) 4.50g
Section 3 Homework

26
Complete the gas laws worksheet
AND #33, 40, 43, 52 on pg. 219-221.
Section 5.4
GAS STOICHIOMETRY
27
Gases and Stoichiometry
Reactions involve moles of
substances.
 Recall that at STP (0ºC and 1 atm)
1mol of any gas occupies 22.4 L.
– At STP this can be a conversion
factor: 1mol/22.4L or 22.4L/1mol
 If not at STP, use the ideal gas law to
calculate moles or volume of a
substance.

28
Section 4 Example
Quicklime (CaO) is produced by the thermal
decomposition of calcium carbonate. Calculate
the volume of carbon dioxide produced at STP
if 152g of calcium carbonate are completely
decomposed.
CaCO3  CaO + CO2
 Convert to moles: 152g x 1mol
= 1.52mol
100.09g
CaCO3
 1:1 mole ratio of CaCO3 to CO2
1.52mol CO2
 Use STP conditions & stoichiometry: Can double
check using
– At STP 1mol = 22.4L
ideal gas
29
– 1.52mol x (22.4L/1mol) = 34.1L CO2
law

Gas Density and Molar Mass
Recall: D = m/V
 Let mmolar stand for molar mass
 mmolar = m/n so n = m/mmolar
 PV = nRT solve for n: n= PV/RT
 Thus m/mmolar = PV/RT
 Solve for mmolar: mmolar = mRT/VP
 Replace m/V with D: mmolar = DRT/P
 If density, temperature, and pressure
are known, molar mass can be found.

30
AP Practice Question
Determine the formula for a gaseous
silane (SinH2n+2) if it’s density is 5.47g/L
at 0ºC and 1.00atm.
*There are several ways to solve!
a)SiH4
b)Si2H6
c)Si3H8
31
d)Si4H10
Section 4 Homework

32
Pg. 220-221 #51, 54, 57, 63, 64
Section 5.5
DALTON’S LAW OF
PARTIAL PRESSURES
33
Dalton’s Law of Partial Pressures
The total pressure in a container is the
sum of the pressure each gas would
exert if it were alone in the container.
 Total pressure = sum of partial
pressures.
 Ptot = P1 + P2 + P3 + ...
– P1, P2, P3 are individual gases
 From the ideal gas law: PTotal = (nTotal)RT
V

34
Partial Pressures Cont.



35
What does Dalton’s Law tell us about
ideal gases?
Total # of gas particles, not their identities,
is important.
– V of individual gas particles doesn’t
affect the total P.
– Forces between gas particles doesn’t
affect the total P.
If these were important, the different
identities of gas particles would affect the
total P differently.
AP Practice Question
A gaseous mixture at 25°C contained 1mol
CH4 and 2mol O2, and P = 2atm. The gases
underwent the following reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What is the P in the container after the
reaction goes to completion and the T is
allowed to return to 25°C?
a)1atm
b)2atm
c)3atm
36
d)4atm
AP Practice Question

A sealed, rigid container is filled with three
identical gases: A, B, and C. The partial
pressure of each gas is known as well as
T and V. What additional information is
needed to find the masses of the gases in
the container?
a) average distance travelled between
molecular collisions
b) the intermolecular forces
c) the molar masses of the gases
37 d) the total pressure
The mole fraction

Ratio of moles of a substance to the
total moles.

symbol is Greek letter chi

c1 =
n1
ntot

38
c
= P1
Ptot
Mole fractions have no units!
AP Practice Question

A reaction makes a mixture of CO2,
CO, and H2O. The gaseous products
contained 0.60mol CO2, 0.30mol CO,
and 0.10mol H2O. If the total P is
0.80atm, what is the partial P of CO?
a) 0.24atm
b) 0.34atm
c) 0.080atm
39 d) 0.13atm
Vapor Pressure
Water evaporates!
 When water evaporates, the resulting
water vapor has a pressure.
– Vapor pressure changes with Tmust be looked up.
 Gases are often collected over water
so the vapor pressure of water must
be subtracted from the total
pressure.
 Vapor pressure must be given.

40
AP Practice Question
A sample of methane gas was collected over
water at 35°C. The sample had a total
pressure of 756mm Hg. Determine the partial
pressure of methane gas in the sample.
(Vapor pressure of water at 35°C is 41mm
Hg.)
a)760mm
Hg
b)41mm Hg
c)715mm Hg
d)797mm Hg
41
Section 5 Homework

42
Pg. 221-222 #65, 67, 69, 72
Collapsing Can Demo


Watch the demonstration.
Why did the can collapse?
-The heat vaporized the water, which in turn
increased P and pushed air out of the can.
-When the can was inverted the water vapor
quickly cooled. This caused a quick drop in P
(created a partial vacuum because essentially
no air was left to maintain P).
-The atmospheric P outside of the can was much
greater than P inside of the can, which allowed
43the can to be crushed.
Section 5.6
THE KINETIC MOLECULAR
THEORY OF GASES
44
Kinetic Molecular Theory (KMT)Explains Behavior & Properties of Gases
1. Gases are made up of molecules or atoms.
2. V of particles can be ignored (very small in
3.
4.
45
5.
comparison to distance b/t particles).
Particles constantly move and collide with
each other and the walls of the container.
Collisions with the walls of the container
cause P of the gas.
Particles don’t attract or repel each other;
when they collide, it’s elastic (no KE is lostit’s transferred).
The average KE is proportional to the Kelvin T.
KMT Cont.
Assumes gases are ideal.
 BUT no gases are truly ideal- they
only approach ideal behavior
(specifically nonpolar gases at low P
and high T).
 In reality, gases DO have V (although
small), and they CAN interact with
each other.
 Even so, assuming ideal behavior
gives us good enough answers
about properties of gases.

46
KMT



47
#3 describes motion; let’s quantify it:
Large! For H2 at
urms = √(3RT/mmolar)
20°C =
– urms is root mean square velocity
2,000m/s
– R value used is 8.314J/molK
– molar mass in kg/mol (b/c J = kgm2/s2)
#5: KE per mole (average KE) = 3/2 RT
- Recall definition of T! Directly related!
- Units: J/mol
KE per molecule = ½ mv2  this is the
only equation given on AP exam!
- Units: J
Root Mean Square Velocity
Example
What is the root mean square
velocity for the atoms in a sample of
He gas at 25°C?
 Convert T to K: 25 + 273 = 298K
 M = 4.00g/mol  0.004000kg/mol
 urms = 136m/s

48
Range of velocities
The average distance a molecule
travels between collisions with another
gas particle is called the mean free
path and is small (near 10-7)
– Results in a range of velocities.
 Temperature is an average. There are
molecules of many speeds in the
average.
 This is shown on a graph called a
49 velocity distribution.

Maxwell-Boltzmann Distribution
number of particles
273 K
50
1273 K
Notice that with higher
T, average velocities
increase and so does
the velocity range.
2273 K
Molecular Velocity
AP Practice Question
Two balloons are at the same T and P.
One contains 14g of nitrogen and the
other contains 20.0g of argon. Which of
the following is true?
a)D
of N2 > D of Ar
b)Average speed of N2 > average speed
of Ar molecules
c)Average KE of N2 molecules > average
KE of Ar molecules
51
d)V of N2 container < V Ar
AP Practice Question
Increasing the T of an ideal gas from
50°C to 75°C at constant V will cause
which of the following to increase for the
gas?
a)average
molecular mass of the gas
b)average distance between molecules
c)average speed of the molecules
d)density of the gas
52
Section 6 Homework

53
Pg. 222-223 #78, 79, 82, 83
Section 5.7
EFFUSION AND DIFFUSION
54
Effusion
Passage of gas through a small hole,
into a vacuum.
 Effusion rate = speed at which the
gas is transferred into the vacuum.
 Graham’s Law - the relative rates of
effusion are inversely proportional to
the square roots of the molar masses
of the gas particles.
Rate of effusion for gas 1
M2

Rate of effusion for gas 2
M1

55
Diffusion
The spreading of a gas through a
room (mixing of gases).
 Slow considering molecules move at
hundreds of meters per second.
– Slower movement is caused by
collisions with other molecules in
the air.
 Best estimate is Graham’s Law.
– Ratio is actually less.
56
– More complex analysis required.

Section 7 Homework

57
Pg. 223 #86, 88
Sections 5.8 & 5.9
REAL GASES
58
Real Gases
Real molecules do take up space and
they do interact with each other
(especially polar molecules).
 Need to add correction factors to the
ideal gas law to account for these.
 a = correction factor for pressure
 b = correction factor for volume

59
Volume Correction



The actual volume free to move in is less
because particles do take up some of the
volume.
More molecules will have more effect
(taking up more space).
Corrected volume V’ = V - nb
– b is a constant that differs for each gas.
 P’
60
=
nRT
(V-nb)
Pressure Correction
Molecules are attracted to each otherpressure on the container will be less
than ideal gases.
 Size of correction factor depends on the
# of molecules per liter (conc. of gas).
 More molecules = closer together and
more likely to interact/attract.
 Since two molecules interact, the effect
must be squared.
2
a=

61
Pobserved = P’ - a
()
n
V
proportionality
constant
All Together



62
Pobs= nRT
V-nb
2
-a n
()
V
Called the Van der Waal’s equation if
rearranged:
2

n

 Pobs + a    x  V - nb  nRT
V 

Corrected
Pressure
Corrected
Volume
NOT given on
AP Equation
sheet!
Graphing Real Gases



63
For ideal
gases PV/nRT
should be 1
(since both
are equal
according to
ideal gas law).
Not seen for
real gases.
Notice the
effect of T on
ideal gas
behavior.
Graphing Real Gases


64
Deviation from
ideal behavior
depends on
identity of the
gas too.
Smaller,
nonpolar gases
exhibit more
ideal behavior.
Where Do Constants Come From?
a and b are experimentally
determined.
 Different for each gas.
 Bigger molecules have larger b.
 a depends on both size and polarity.
 Note: table of constants for some
gases is on pg. 210 in the book.

65
Graphing Real Gases

Take a closer look at H2 on the graph.
– Most ideal behavior, so it has lowest ‘a’
value of the gases shown for Van der Waals
equation.
– Lower a means less correction needed.
– Thus it must have weak intermolecular
forces.

66
Real gas behavior can tell us how big of
a role intermolecular forces play in
attraction between gas molecules.
AP Practice Question
The true volume of a real gas is
smaller than that calculated from the
ideal gas equation. This occurs
because the ideal gas equation does
not consider which of the following?
a)Attraction
67
between molecules
b)Shapes of molecules
c)Volume of molecules
d)Mass of molecules
AP Practice Question
Which of the following gases probably
shows the greatest deviation from
ideal gas behavior?
a)
b)
c)
d)
68
He
O2
SF4
SiH4
Sections 8&9 Homework

69
Pg. 223 #89, 90